The method of compressive sensing is applied to moving source data created by simulation to estimate the mode wavenumbers, mode depth functions and mode amplitudes without any environmental acoustic information, such as sound speed profile or bottom properties. The method needs in principle only data covering a short range span and is thus applicable to a range-dependent environment to estimate the properties of the local modes (as a function of range). It yields very accurate estimates of mode wavenumbers in simulation, and approximate estimates of mode depth functions and mode amplitudes due to the non-linear nature of the CS method.